Bernstein Inequality for the Riesz Derivative of Order \(0<\alpha<1\) of Entire Functions of Exponential Type in the Uniform Norm

We consider Bernstein’s inequality for the Riesz derivative of order \(0<\alpha<1\) of entire functions of exponential type in the uniform norm on the real line. For this operator, the corresponding interpolation formula is obtained; this formula has nonequidistant nodes. Using this formula, the sharp Bernstein inequality is obtained for all \(0<\alpha<1\) ; namely, the extremal entire function and the sharp constant are written out.